Manifold mapping optimization with of without true gradients

Manifold mapping optimization with of without true gradients

Delinchant, B.
Lahaye, D.
Wurtz, F.
Coulomb, J.L.

Electrical Engineering, Mathematics and Computer Science

2012-04-30

This paper deals with the Space Mapping optimization algorithms in general and with the Manifold Mapping technique in particular. The idea of such algorithms is to optimize a model with a minimum number of each objective function evaluations using a less accurate but faster model. In this optimization procedure, fine and coarse models interact at each iteration in order to adjust themselves in order to converge to the real optimum. The Manifold Mapping technique guarantees mathematically this convergence but requires gradients of both fine and coarse model. Approximated gradients can be used for some cases but are subject to divergence. True gradients can be obtained for many numerical model using adjoint techniques, symbolic or automatic differentiation. In this context, we have tested several Manifold Mapping variants and compared their convergence in the case of real magnetic device optimization.

space mapping
manifold mapping
optimization
surrogate model
gradients
symbolic derivation
automatic differentiation

http://resolver.tudelft.nl/uuid:a53f5bbd-2640-41cb-982d-b05a6fff9166

Delft University of Technology, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft Institute of Applied Mathematics

1389-6520

Reports of the Department of Applied Mathematical Analysis, 12-05

Institutional Repository

report

(c)2012 Delinchant, B., Lahaye, D., Wurtz, F., Coulomb, J.L.